Re: Obections to Cantor's Theory (Wikipedia article)

Chris Menzel said:
> On Tue, 26 Jul 2005 16:39:58 -0400, Tony Orlow <aeo6@xxxxxxxxxxx> said:
> > ...
> > The big problem in transfinite cardinality is the assumption that a
> > bijection necessarily indicates equal sizes for infinite sets, as it
> > does for finite sets.
>
> It's not an assumption, it's a definition, one that you reject. That's
> fine, but until you provide equally rigorous alternatives, it's the only
> game in town. And frankly, you've got no business rejecting it just
> because some of the consequences conflict with your intuitions. The
> mathematics of the infinite is occasionally surprising, especially when
> one doesn't have a complete understanding of the subject matter.
>
> > When the only way to form a bijection is with a mapping function,
>
> How else?
>
> > then that function needs to be taken into account. This nonsense
> > about an infinite set of finite whole numbers is pretty bad too, but
> > probably without any real consequences.
>
> You seem to agree that the set of whole numbers is infinite. But there
> was an inductive argument a few posts back that all the whole numbers
> are finite, and hence that the set of finite whole numbers is infinite.
> There was some real mathematics there. Why have you not responded to a
> mathematical proof that all the members of the infinite set of whole
> numbers are finite? It would be your chance to show everyone where the
> error in the argument lies.
>
> Chris Menzel
>
>
I have repsonded to that proof over and over. Where were you when we were
discussing the nature of inductive proof, and the implicit infinite loop in the
construction that no one seems to have considered, and the fact that adding 1
an infinite number of times, as is done in the generation of the infinite set
of naturals, produces an infinite sum?

I tell you what. You refute my inductive proof that the set of naturals is
finite, without refuting your own proof, and then we'll talk. Good luck. I
don't expect any response, since you folks tend to ignore any proof you can't
throw "largest finite" at. Your bag of tricks is really rather finite, and more
and more transparent.
--
Smiles,

Tony
.

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